IMAGE ENHANCEMENT IN THE FREQUENCY DOMAIN (1)
|
|
|
- Arleen Goodwin
- 5 years ago
- Views:
Transcription
1 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek IMAGE ENHANCEMENT IN THE FREQUENCY DOMAIN KOM3 Image Processing in Indstrial Systems Some of the contents are adopted from R. C. Gonzalez R. E. Woods Digital Image Processing nd edition Prentice Hall 008
2 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek Qestions In-depth nderstanding Why do we need to condct image processing in the freqency domain? What does Forier series do? Properties Is FT a linear or nonlinear process? What wold the FT of a rotated image look like? What is FFT? What is F00? Why is image padding necessary?
3 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek 3 Forier series The Forier transform can separate the freqencies which contribte to the signal which is emitted from the image slice. Crcially it also tells s the amplitde of those waes which will correspond to signal intensity leels in an image.
4 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek 4 Forier series s Forier Transform Any fnction that periodically repeats itself can be expressed as the sm of sines and/or cosines of different freqencies each mltiplied by a different coefficient Forier series. Een fnctions that are not periodic bt whose area nder the cre is finite can be expressed as the integral of sines and/or cosines mltiplied by a weighting fnction Forier transform.
5 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek 5 What is the freqency domain
6 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek 6 What is the freqency domain? The freqency domain refers to the plane of the two dimensional discrete Forier transform of an image. The prpose of the Forier transform is to represent a signal as a linear combination of sinsoidal signals of arios freqencies.
7 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek 7 Continos FT The one-dimensional Forier transform and its inerse F Forier transform continos case Inerse Forier transform: f x F e jx d The two-dimensional Forier transform and its inerse Forier transform continos case F f x f x e jx f x dx y e Inerse Forier transform: y F e where j j xy j xy dxdy dd e j cos jsin
8 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek 8 Discrete FT DFT The one-dimensional Forier transform and its inerse Forier transform discrete case F M M x0 f x e jx/ M Inerse Forier transform: M f x 0 F e jx/ M for for 0... M x 0... M
9 Discrete FT DFT 9 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek F can be expressed in polar coordinates: R: the real part of F I: the imaginary part of F Power spectrm: phase angle or phase spectrm tan magnitde or spectrm where R I I R F e F F j
10 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek 0 Discrete FT DFT e j cos j sin discrete Forier transform can be redefined F M M x0 f x[cos x / M j sin x / M ] Freqency time domain: the domain ales of oer which the ales of F range; becase determines the freqency of the components of the transform. Freqency time component: each of the M terms of F.
11 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek Discrete FT DFT The two-dimensional Forier transform and its inerse Forier transform discrete case F MN M N x0 y0 f x y e 0... M 0... N j x / M y / N Inerse Forier transform: f x y M N 0 0 F e j x / M y / N x 0... M y 0... N : the transform or freqency ariables x y : the spatial or image ariables
12 Discrete FT DFT KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek We define the Forier spectrm phase angle and power spectrm as follows: R: the real part of F I: the imaginary part of F spectrm power phaseangle tan spectrm I R F P R I I R F
13 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek 3 Discrete FT DFT magnitde phase
14 Some properties of Forier transform 4 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek symmetric conjgate symmetric * aerage 00 shift 0 0 F F F F y x f MN F N M F y x f M x N y y x F
15 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek 5 Some properties of Forier transform Spatial Domain x y Freqency Domain Linearity c f x y cgx y c F cg Scaling ax by f F ab a b Shifting f x x0 y y 0 j x0 y0 e F Shifting for a period x y f x y F M / N / Symmetry F F Conoltion f x y gx y F G
16 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek 6 Conoltion in Forier transform Spatial Domain x Freqency Domain g f h G FH g fh G F H So we can find gx by Forier transform g f h IFT FT FT G F H
17 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek 7 FT examples rectx fnction sincx=sinx/x
18 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek 8 FT examples
19 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek 9 FT examples Typically we isalize F Typically we isalize F
20 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek 0 FT examples DFT DFT
21 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek FT examples Sine wae Its DFT D Gassian fnction Its DFT
22 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek Image processing in the Freqency domain f x y x y g x y x y
23 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek 3 Image processing in the Freqency domain Noise redction in the freqency domain
24 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek 4 Image processing in the Freqency domain. Take the FT of fx:. Remoe ndesired freqencies: 3. Conert back to a signal
25 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek 5 Image processing in the Freqency domain We want a smoothed fnction of fx g x f xhx Let s se a Gassian kernel hx Then h x H G x exp exp FH H x H attenates high freqencies in F Low-pass Filter!
26 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek 6 Image s. its freqency domain representation Magnitde of the FT Does not look anything like what we hae seen
27 KOM3 Image Processing in Indstrial Systems Dr Mharrem Mercimek 7 Image s. its freqency domain representation
Image Restoration Image Degradation and Restoration
Image Degradation and Restoration hxy Image Degradation Model: Spatial domain representation can be modeled by: g x y h x y f x y x y Freqency domain representation can be modeled by: G F N Prepared By:
Digital Image Processing Chapter 5: Image Restoration
Digital Image Processing Chapter 5: Image Restoration Concept of Image Restoration Image restoration is to restore a degraded image back to the original image while image enhancement is to maniplate the
Spatial domain: Enhancement in the case of a single image
Unit-6 Spatial domain: Enhancement in the case of a single image Spatial masks Man image enhancement techniqes are based on spatial operations performed on local neighborhoods of inpt piels. The image
Digital Image Processing Chapter 5: Image Restoration
Digital Image Processing Chapter 5: Image Restoration Concept of Image Restoration Image restoration is to restore a degraded image back to the original image while image enhancement is to maniplate the
Lecture 5: Frequency Domain Transformations
#1 Lecture 5: Frequency Domain Transformations Saad J Bedros sbedros@umn.edu From Last Lecture Spatial Domain Transformation Point Processing for Enhancement Area/Mask Processing Transformations Image
Image Operations in the Frequency Domain
Image Processing Image Operations in the Freqenc Domain Freqenc Bands Low Pass Filter High Pass Filter Band pass Filter Blrring Sharpening Image Forier Spectrm Percentage of image power enclosed in circles
Biomedical Image Analysis. Spatial Filtering
Biomedical Image Analysis Contents: Spatial Filtering The mechanics of Spatial Filtering Smoothing and sharpening filters BMIA 15 V. Roth & P. Cattin 1 The Mechanics of Spatial Filtering Spatial filter:
Image Enhancement in the Frequency Domain Periodicity and the need for Padding:
Prepared B: Dr. Hasan Demirel PhD Image Enhancement in the Freqenc Domain Periodicit and the need for Padding: Periodicit propert of the DFT: The discrete Forier Transform and the inverse Forier transforms
COMP 9517 Computer Vision
COMP 9517 Computer Vision Frequency Domain Techniques 1 Frequency Versus Spa
f x y z ds f P S (,, ) lim ( ) ds f P S S S.
4.7 rface Integral We diide srface into patches patch, mltiply by the area with area, and form the sm n n i j f P ( ). We ealate f at a point P, in each Then we take the limit as the patch size approaches
Degraded digital image restoration Spatial domain processing Additive noise Frequency domain Blurred image
Image Comm. Lab EE/NTHU 1 Chapter 5 Image Restoration Degraded digital image restoration Spatial domain processing Additie noise Freqency domain Blrred image Image Comm. Lab EE/NTHU 2 5. 1 Model of Image
Texture. Outline. Image representations: spatial and frequency Fourier transform Frequency filtering Oriented pyramids Texture representation
Texture Outline Image representations: spatial and frequency Fourier transform Frequency filtering Oriented pyramids Texture representation 1 Image Representation The standard basis for images is the set
Image Enhancement in Spatial Domain. By Dr. Rajeev Srivastava
Image Enhancement in Spatial Domain By Dr. Rajeev Srivastava CONTENTS Image Enhancement in Spatial Domain Spatial Domain Methods 1. Point Processing Functions A. Gray Level Transformation functions for
Computer Vision 2. SS 18 Dr. Benjamin Guthier Professur für Bildverarbeitung. Computer Vision 2 Dr. Benjamin Guthier
Computer Vision 2 SS 18 Dr. Benjamin Guthier Professur für Bildverarbeitung Computer Vision 2 Dr. Benjamin Guthier 1. IMAGE PROCESSING Computer Vision 2 Dr. Benjamin Guthier Content of this Chapter Non-linear
Digital Image Processing. Lecture 6
Digital Image Processing Lecture 6 (Enhancement in the Frequency domain) Bu-Ali Sina University Computer Engineering Dep. Fall 2016 Image Enhancement In The Frequency Domain Outline Jean Baptiste Joseph
Lecture 10. Diffraction. incident
1 Introdction Lectre 1 Diffraction It is qite often the case that no line-of-sight path exists between a cell phone and a basestation. In other words there are no basestations that the cstomer can see
Spatial domain processing Remove the additive noise Frequency domain
Image Comm. Lab EE/NTHU 1 Chapter 5 Image Restoration and Reconstrction Degraded digital image restoration Spatial domain processing Remoe the additie noise Freqency domain Highlight ht the blrred image
5. The angle of elevation of the top of a tower from a point 120maway from the. What are the x-coordinates of the maxima of this function?
Exams,Math 141,Pre-Calculus, Dr. Bart 1. Let f(x) = 4x+6. Find the inverse of f algebraically. 5x 2. Suppose f(x) =x 2.We obtain g(x) fromf(x) by translating to the left by 2 translating up by 3 reecting
UNIT 3 EXPRESSIONS AND EQUATIONS Lesson 3: Creating Quadratic Equations in Two or More Variables
Guided Practice Example 1 Find the y-intercept and vertex of the function f(x) = 2x 2 + x + 3. Determine whether the vertex is a minimum or maximum point on the graph. 1. Determine the y-intercept. The
Warm-Up Exercises. Find the x-intercept and y-intercept 1. 3x 5y = 15 ANSWER 5; y = 2x + 7 ANSWER ; 7
Warm-Up Exercises Find the x-intercept and y-intercept 1. 3x 5y = 15 ANSWER 5; 3 2. y = 2x + 7 7 2 ANSWER ; 7 Chapter 1.1 Graph Quadratic Functions in Standard Form A quadratic function is a function that
Image Representation
Image Representation SS 008 Image Processing Multimedia Computing, Uniersität Augsburg Rainer.Lienhart@informatik.uni-augsburg.de www.multimedia-computing.{de,org} Reference Bernd Jähne. Digital Image
FPGA Implementation of Discrete Fourier Transform Using CORDIC Algorithm
AMSE JOURNALS-AMSE IIETA publication-2017-series: Advances B; Vol. 60; N 2; pp 332-337 Submitted Apr. 04, 2017; Revised Sept. 25, 2017; Accepted Sept. 30, 2017 FPGA Implementation of Discrete Fourier Transform
Computer Vision and Graphics (ee2031) Digital Image Processing I
Computer Vision and Graphics (ee203) Digital Image Processing I Dr John Collomosse J.Collomosse@surrey.ac.uk Centre for Vision, Speech and Signal Processing University of Surrey Learning Outcomes After
Biomedical Image Analysis. Point, Edge and Line Detection
Biomedical Image Analysis Point, Edge and Line Detection Contents: Point and line detection Advanced edge detection: Canny Local/regional edge processing Global processing: Hough transform BMIA 15 V. Roth
Statistical Image Compression using Fast Fourier Coefficients
Statistical Image Compression using Fast Fourier Coefficients M. Kanaka Reddy Research Scholar Dept.of Statistics Osmania University Hyderabad-500007 V. V. Haragopal Professor Dept.of Statistics Osmania
Multimedia Computing: Algorithms, Systems, and Applications: Edge Detection
Multimedia Computing: Algorithms, Systems, and Applications: Edge Detection By Dr. Yu Cao Department of Computer Science The University of Massachusetts Lowell Lowell, MA 01854, USA Part of the slides
Image Reconstruction from Projection
Image Reconstruction from Projection Reconstruct an image from a series of projections X-ray computed tomography (CT) Computed tomography is a medical imaging method employing tomography where digital
COORDINATE GEOMETRY CHANGE OF AXES EXERCISE 1. The point to which the origin should be shifted in order to eliminate x and y terms in the equation 4x 9y 8x 36y 4 0 is (1, ) ( 4, ( 1,) 4) (1, ). In order
Chapter 3: Intensity Transformations and Spatial Filtering
Chapter 3: Intensity Transformations and Spatial Filtering 3.1 Background 3.2 Some basic intensity transformation functions 3.3 Histogram processing 3.4 Fundamentals of spatial filtering 3.5 Smoothing
Image Warping, Compositing & Morphing
Image Processing Image Warping, Compositing & Morphing Adam Finkelstein Princeton Uniersit COS 426, Spring 2005 Image Processing Qantization Uniform Qantization Random dither Ordered dither Flod-Steinberg
MAC2313 Test 3 A E g(x, y, z) dy dx dz
MAC2313 Test 3 A (5 pts) 1. If the function g(x, y, z) is integrated over the cylindrical solid bounded by x 2 + y 2 = 3, z = 1, and z = 7, the correct integral in Cartesian coordinates is given by: A.
Lecture 2: 2D Fourier transforms and applications
Lecture 2: 2D Fourier transforms and applications B14 Image Analysis Michaelmas 2017 Dr. M. Fallon Fourier transforms and spatial frequencies in 2D Definition and meaning The Convolution Theorem Applications
MH2800/MAS183 - Linear Algebra and Multivariable Calculus
MH28/MAS83 - Linear Algebra and Multivariable Calculus SEMESTER II EXAMINATION 2-22 Solved by Tao Biaoshuai Email: taob@e.ntu.edu.sg QESTION Let A 2 2 2. Solve the homogeneous linear system Ax and write
EECS 487: Interactive Computer Graphics f
Interpolating Key Vales EECS 487: Interactive Compter Graphics f Keys Lectre 33: Keyframe interpolation and splines Cbic splines The key vales of each variable may occr at different frames The interpolation
Reading. 2. Fourier analysis and sampling theory. Required: Watt, Section 14.1 Recommended:
Reading Required: Watt, Section 14.1 Recommended: 2. Fourier analysis and sampling theory Ron Bracewell, The Fourier Transform and Its Applications, McGraw-Hill. Don P. Mitchell and Arun N. Netravali,
Fourier transform of images
Fourier transform of images Stefano Ferrari Università degli Studi di Milano stefano.ferrari@unimi.it Methods for Image Processing academic year 2014 2015 Extension to bidimensional domain The concepts
To graph the point (r, θ), simply go out r units along the initial ray, then rotate through the angle θ. The point (1, 5π 6
Polar Coordinates Any point in the plane can be described by the Cartesian coordinates (x, y), where x and y are measured along the corresponding axes. However, this is not the only way to represent points
What will we learn? Neighborhood processing. Convolution and correlation. Neighborhood processing. Chapter 10 Neighborhood Processing
What will we learn? Lecture Slides ME 4060 Machine Vision and Vision-based Control Chapter 10 Neighborhood Processing By Dr. Debao Zhou 1 What is neighborhood processing and how does it differ from point
Edge and local feature detection - 2. Importance of edge detection in computer vision
Edge and local feature detection Gradient based edge detection Edge detection by function fitting Second derivative edge detectors Edge linking and the construction of the chain graph Edge and local feature
KINEMATICS OF FLUID MOTION
KINEMATICS OF FLUID MOTION The Velocity Field The representation of properties of flid parameters as fnction of the spatial coordinates is termed a field representation of the flo. One of the most important
Lecture Image Enhancement and Spatial Filtering
Lecture Image Enhancement and Spatial Filtering Harvey Rhody Chester F. Carlson Center for Imaging Science Rochester Institute of Technology rhody@cis.rit.edu September 29, 2005 Abstract Applications of
JNTUWORLD. 4. Prove that the average value of laplacian of the equation 2 h = ((r2 σ 2 )/σ 4 ))exp( r 2 /2σ 2 ) is zero. [16]
![JNTUWORLD. 4. Prove that the average value of laplacian of the equation 2 h = ((r2 σ 2 )/σ 4 ))exp( r 2 /2σ 2 ) is zero. [16]](/thumbs/78/78591353.jpg "JNTUWORLD. 4. Prove that the average value of laplacian of the equation 2 h = ((r2 σ 2 )/σ 4 ))exp( r 2 /2σ 2 ) is zero. [16]")
Code No: 07A70401 R07 Set No. 2 1. (a) What are the basic properties of frequency domain with respect to the image processing. (b) Define the terms: i. Impulse function of strength a ii. Impulse function
Chapter 11 Image Processing
Chapter Image Processing Low-level Image Processing Operates directly on a stored image to improve or enhance it. Stored image consists of a two-dimensional array of pixels (picture elements): Origin (0,
Filtering. -If we denote the original image as f(x,y), then the noisy image can be denoted as f(x,y)+n(x,y) where n(x,y) is a cosine function.
Filtering -The image shown below has been generated by adding some noise in the form of a cosine function. -If we denote the original image as f(x,y), then the noisy image can be denoted as f(x,y)+n(x,y)
AP Calculus AB Unit 2 Assessment
Class: Date: 203-204 AP Calculus AB Unit 2 Assessment Multiple Choice Identify the choice that best completes the statement or answers the question. A calculator may NOT be used on this part of the exam.
The azimuth-dependent offset-midpoint traveltime pyramid in 3D HTI media
The azimuth-dependent offset-midpoint traeltime pyramid in 3D HTI media Item Type Conference Paper Authors Hao Qi; Stoas Alexey; Alkhalifah Tariq Ali Eprint ersion Publisher's Version/PDF DOI.9/segam3-58.
PARAMETRIC EQUATIONS AND POLAR COORDINATES
10 PARAMETRIC EQUATIONS AND POLAR COORDINATES PARAMETRIC EQUATIONS & POLAR COORDINATES A coordinate system represents a point in the plane by an ordered pair of numbers called coordinates. PARAMETRIC EQUATIONS
Two-Dimensional Fourier Transform and Linear Filtering
Yao Wang 7 EL-GY 63: Image and Video Processing Two-Dimensional Forier Transorm and Linear Filtering Yao Wang Tandon School o Engineering New York Uniersit Yao Wang 7 EL-GY 63: Image and Video Processing
3. Image formation, Fourier analysis and CTF theory. Paula da Fonseca
3. Image formation, Fourier analysis and CTF theory Paula da Fonseca EM course 2017 - Agenda - Overview of: Introduction to Fourier analysis o o o o Sine waves Fourier transform (simple examples of 1D
To graph the point (r, θ), simply go out r units along the initial ray, then rotate through the angle θ. The point (1, 5π 6. ) is graphed below:
Polar Coordinates Any point in the plane can be described by the Cartesian coordinates (x, y), where x and y are measured along the corresponding axes. However, this is not the only way to represent points
Advances in Environmental Biology
AESI Jornals Advances in Environmental Biology ISS-1995-0756 EISS-1998-1066 Jornal home page: http://www.aensiweb.com/aeb/ The Generic Mathematical Model of Freency Sampling Digital Filters with Shiftable
Magnetics. Introduction to Filtering using the Fourier Transform. Chuck Connor, Laura Connor. Potential Fields. Magnetics.
Introduction to using the Chuck Connor, Laura Connor Potential Fields for this week Nm Sm Schematic Earth dipolar magnetic field. The field lines placed in the page plane are drawn as thick lines, those
Digital Image Processing
Digital Image Processing Jen-Hui Chuang Department of Computer Science National Chiao Tung University 2 3 Image Enhancement in the Spatial Domain 3.1 Background 3.4 Enhancement Using Arithmetic/Logic Operations
Autoregressive and Random Field Texture Models
1 Autoregressive and Random Field Texture Models Wei-Ta Chu 2008/11/6 Random Field 2 Think of a textured image as a 2D array of random numbers. The pixel intensity at each location is a random variable.
4.2 Graphing Inverse Trigonometric Functions
4.2 Graphing Inverse Trigonometric Functions Learning Objectives Understand the meaning of restricted domain as it applies to the inverses of the six trigonometric functions. Apply the domain, range and
Analysis of Planar Anisotropy of Fibre Systems by Using 2D Fourier Transform
Maroš Tunák, Aleš Linka Technical University in Liberec Faculty of Textile Engineering Department of Textile Materials Studentská 2, 461 17 Liberec 1, Czech Republic E-mail: maros.tunak@tul.cz ales.linka@tul.cz
Coordinate Transformations in Advanced Calculus
Coordinate Transformations in Advanced Calculus by Sacha Nandlall T.A. for MATH 264, McGill University Email: sacha.nandlall@mail.mcgill.ca Website: http://www.resanova.com/teaching/calculus/ Fall 2006,
Image Enhancement: To improve the quality of images
Image Enhancement: To improve the quality of images Examples: Noise reduction (to improve SNR or subjective quality) Change contrast, brightness, color etc. Image smoothing Image sharpening Modify image
Area and Volume. where x right and x left are written in terms of y.
Area and Volume Area between two curves Sketch the region and determine the points of intersection. Draw a small strip either as dx or dy slicing. Use the following templates to set up a definite integral:
EE795: Computer Vision and Intelligent Systems
EE795: Computer Vision and Intelligent Systems Spring 2012 TTh 17:30-18:45 WRI C225 Lecture 02 130124 http://www.ee.unlv.edu/~b1morris/ecg795/ 2 Outline Basics Image Formation Image Processing 3 Intelligent
Central Slice Theorem
Central Slice Theorem Incident X-rays y f(x,y) R x r x Detected p(, x ) The thick line is described by xcos +ysin =R Properties of Fourier Transform F [ f ( x a)] F [ f ( x)] e j 2 a Spatial Domain Spatial
Date: December 5, 1999 Dist'n: T1E1.4
12/4/99 1 T1E14/99-559 Project: T1E14: VDSL Title: Vectored VDSL (99-559) Contact: J Cioffi, G Ginis, W Y Dept of EE, Stanford U, Stanford, CA 945 Cioffi@stanforded, 1-65-723-215, F: 1-65-724-3652 Date:
Issues with Curve Detection Grouping (e.g., the Canny hysteresis thresholding procedure) Model tting They can be performed sequentially or simultaneou
an edge image, nd line or curve segments present Given the image. in Line and Curves Detection 1 Issues with Curve Detection Grouping (e.g., the Canny hysteresis thresholding procedure) Model tting They
Image Processing. Application area chosen because it has very good parallelism and interesting output.
Chapter 11 Slide 517 Image Processing Application area chosen because it has very good parallelism and interesting output. Low-level Image Processing Operates directly on stored image to improve/enhance
Section 7.6 Graphs of the Sine and Cosine Functions
Section 7.6 Graphs of the Sine and Cosine Functions We are going to learn how to graph the sine and cosine functions on the xy-plane. Just like with any other function, it is easy to do by plotting points.
COMP30019 Graphics and Interaction Transformation geometry and homogeneous coordinates
COMP30019 Graphics and Interaction Transformation geometry and homogeneous coordinates Department of Computer Science and Software Engineering The Lecture outline Introduction Vectors and matrices Translation
Image Compression Compression Fundamentals
Compression Fndamentals Data compression refers to the process of redcing the amont of data reqired to represent given qantity of information. Note that data and information are not the same. Data refers
Fourier analysis and sampling theory
Reading Required: Shirley, Ch. 9 Recommended: Fourier analysis and sampling theory Ron Bracewell, The Fourier Transform and Its Applications, McGraw-Hill. Don P. Mitchell and Arun N. Netravali, Reconstruction
Polar Coordinates. Chapter 10: Parametric Equations and Polar coordinates, Section 10.3: Polar coordinates 27 / 45
: Given any point P = (x, y) on the plane r stands for the distance from the origin (0, 0). θ stands for the angle from positive x-axis to OP. Polar coordinate: (r, θ) Chapter 10: Parametric Equations
Digital Image Processing
Digital Image Processing Third Edition Rafael C. Gonzalez University of Tennessee Richard E. Woods MedData Interactive PEARSON Prentice Hall Pearson Education International Contents Preface xv Acknowledgments
IB-2 Polarization Practice
Name: 1. Plane-polarized light is incident normally on a polarizer which is able to rotate in the plane perpendicular to the light as shown below. In diagram 1, the intensity of the incident light is 8
Algebra 2 Honors Lesson 10 Translating Functions
Algebra 2 Honors Lesson 10 Translating Functions Objectives: The students will be able to translate a base function horizontally and vertically. Students will be able to describe the translation of f(x)
CS1114 Section 8: The Fourier Transform March 13th, 2013
CS1114 Section 8: The Fourier Transform March 13th, 2013 http://xkcd.com/26 Today you will learn about an extremely useful tool in image processing called the Fourier transform, and along the way get more
Edge detection. Convert a 2D image into a set of curves. Extracts salient features of the scene More compact than pixels
Edge Detection Edge detection Convert a 2D image into a set of curves Extracts salient features of the scene More compact than pixels Origin of Edges surface normal discontinuity depth discontinuity surface
MATH 31A HOMEWORK 9 (DUE 12/6) PARTS (A) AND (B) SECTION 5.4. f(x) = x + 1 x 2 + 9, F (7) = 0
FROM ROGAWSKI S CALCULUS (2ND ED.) SECTION 5.4 18.) Express the antiderivative F (x) of f(x) satisfying the given initial condition as an integral. f(x) = x + 1 x 2 + 9, F (7) = 28.) Find G (1), where
AP Calculus Summer Review Packet
AP Calculus Summer Review Packet Name: Date began: Completed: **A Formula Sheet has been stapled to the back for your convenience!** Email anytime with questions: danna.seigle@henry.k1.ga.us Complex Fractions
Image Restoration. CS 663, Ajit Rajwade
Image Restoration CS 663 Ajit Rajwade Contents Introdction to image restoration Inerse ilter Spread spectrm ilters coded apertre camera and ltter-shtter camera Wiener ilter aim assmptions ormla and deriation
5. Feature Extraction from Images
5. Feature Extraction from Images Aim of this Chapter: Learn the Basic Feature Extraction Methods for Images Main features: Color Texture Edges Wie funktioniert ein Mustererkennungssystem Test Data x i
6. Find the equation of the plane that passes through the point (-1,2,1) and contains the line x = y = z.
Week 1 Worksheet Sections from Thomas 13 th edition: 12.4, 12.5, 12.6, 13.1 1. A plane is a set of points that satisfies an equation of the form c 1 x + c 2 y + c 3 z = c 4. (a) Find any three distinct
Computer Vision. Fourier Transform. 20 January Copyright by NHL Hogeschool and Van de Loosdrecht Machine Vision BV All rights reserved
Van de Loosdrecht Machine Vision Computer Vision Fourier Transform 20 January 2017 Copyright 2001 2017 by NHL Hogeschool and Van de Loosdrecht Machine Vision BV All rights reserved j.van.de.loosdrecht@nhl.nl,
Computer Vision: 4. Filtering. By I-Chen Lin Dept. of CS, National Chiao Tung University
Computer Vision: 4. Filtering By I-Chen Lin Dept. of CS, National Chiao Tung University Outline Impulse response and convolution. Linear filter and image pyramid. Textbook: David A. Forsyth and Jean Ponce,
Name Trigonometric Functions 4.2H
TE-31 Name Trigonometric Functions 4.H Ready, Set, Go! Ready Topic: Even and odd functions The graphs of even and odd functions make it easy to identify the type of function. Even functions have a line
SYNTHETIC APERTURE SIGNAL PROCESSING FOR HIGH RESOLUTION 3D IMAGE RECONSTRUCTION IN THE THZ-DOMAIN
7th Eropean Signal Processing Conference (EUSIPCO 9) Glasgow, Scotland, Agst -8, 9 SYNTHETIC APERTURE SIGNAL PROCESSING FOR HIGH RESOLUTION D IMAGE RECONSTRUCTION IN THE THZ-DOMAIN Marijke Vandewal, Roel
Edge Detection Lecture 03 Computer Vision
Edge Detection Lecture 3 Computer Vision Suggested readings Chapter 5 Linda G. Shapiro and George Stockman, Computer Vision, Upper Saddle River, NJ, Prentice Hall,. Chapter David A. Forsyth and Jean Ponce,
AP * Calculus Review. Area and Volume
AP * Calculus Review Area and Volume Student Packet Advanced Placement and AP are registered trademark of the College Entrance Examination Board. The College Board was not involved in the production of,
2009 Conference for Visual Media Production
009 Conference for Visual Media Production COECTIG SHAPESS VAIATIOS I STEEO IMAGE PAIS C. Doutre and P. asiopoulos Departement of Electrical and Computer gineering Uniersity of British Columbia, Vancouer,
CHAPTER 2: More on Functions
MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 2: More on Functions 2.1 Increasing, Decreasing, and Piecewise Functions; Applications 2.2 The Algebra of Functions 2.3
Exercise: Simulating spatial processing in the visual pathway with convolution
Exercise: Simulating spatial processing in the visual pathway with convolution This problem uses convolution to simulate the spatial filtering performed by neurons in the early stages of the visual pathway,
AQA GCSE Further Maths Topic Areas
AQA GCSE Further Maths Topic Areas This document covers all the specific areas of the AQA GCSE Further Maths course, your job is to review all the topic areas, answering the questions if you feel you need
Function f. Function f -1
Page 1 REVIEW (1.7) What is an inverse function? Do all functions have inverses? An inverse function, f -1, is a kind of undoing function. If the initial function, f, takes the element a to the element
Introduction to Computer Vision. Week 3, Fall 2010 Instructor: Prof. Ko Nishino
Introduction to Computer Vision Week 3, Fall 2010 Instructor: Prof. Ko Nishino Last Week! Image Sensing " Our eyes: rods and cones " CCD, CMOS, Rolling Shutter " Sensing brightness and sensing color! Projective
3.4& Fundamentals& mechanics of spatial filtering(page 166) Spatial filter(mask) Filter coefficients Filter response
Image enhancement in the spatial domain(3.4-3.7) SLIDE 1/21 3.4& 3.4.1 Fundamentals& mechanics of spatial filtering(page 166) Spatial filter(mask) Filter coefficients Filter response Example: 3 3mask Linear
State the domain and range of the relation. EX: {(-1,1), (1,5), (0,3)} 1 P a g e Province Mathematics Southwest TN Community College
A relation is a set of ordered pairs of real numbers. The domain, D, of a relation is the set of all first coordinates of the ordered pairs in the relation (the xs). The range, R, of a relation is the
EE123 Digital Signal Processing
Multi-Dimensional Signals EE23 Digital Signal Processing Lecture Our world is more complex than D Images: f(x,y) Videos: f(x,y,t) Dynamic 3F scenes: f(x,y,z,t) Medical Imaging 3D Video Computer Graphics
EEM 463 Introduction to Image Processing. Week 3: Intensity Transformations
EEM 463 Introduction to Image Processing Week 3: Intensity Transformations Fall 2013 Instructor: Hatice Çınar Akakın, Ph.D. haticecinarakakin@anadolu.edu.tr Anadolu University Enhancement Domains Spatial
EECS490: Digital Image Processing. Lecture #16
Lecture #16 Wiener Filters Constrained Least Squares Filter Computed Tomography Basics Reconstruction and the Radon Transform Fourier Slice Theorem Filtered Backprojections Fan Beams Motion Blurring Model
FUNCTIONS. L f(2)= 2. g(-3)= _ 3. f(t+l)= _. g(x) ) in for x in the outside function (in this case, f(x)).
FUNCTIONS To evaluate a function for a given value, simply plug the value into the function for x. Recall: (f 0 g ) (x) = f(g(x)) OR f[g(x)] read 'Jofg of x" Means to plug the inside function (in this
Towards applications based on measuring the orbital angular momentum of light
CHAPTER 8 Towards applications based on measring the orbital anglar momentm of light Efficient measrement of the orbital anglar momentm (OAM) of light has been a longstanding problem in both classical
Novel Image Fusion Techniques using DCT
nternational Jornal o Compter Science and Bsiness normatics oel mage Fsion Techniqes sing DCT V. P. S. aid SDF Lab CSR-AL Bangalore ABSTRACT Si dierent noel image sion techniqes sing discrete Cosine transorm
2 Unit Bridging Course Day 10
1 / 31 Unit Bridging Course Day 10 Circular Functions III The cosine function, identities and derivatives Clinton Boys / 31 The cosine function The cosine function, abbreviated to cos, is very similar